The UK did claim Canada, along with most of North America, in the Royal Proclamation of 1763. Canada was granted progressively more autonomy over time but the UK still maintained ultimate sovereignty until the Canadian constitution was patriated. The UK effectively ceded its sovereignty over Canada when UK parliament passed the Canada Act 1982.
Denmark granted Greenland autonomy with the 2009 Act on Greenland Self-Government, but Denmark still maintains the authority to modify Greenland's constitutional arrangement. So, much like the UK still held sovereignty over Canada prior to 1982, Denmark still holds sovereignty over Greenland. Apparently there have been some efforts to draft a constitution for Greenland, but that has not been passed into law by Greenland's lawmakers nor has it been patriated by Denmark.
Not really either. While greenland and the others are highly autonomous and practically their own countries, national security is not in their competence but instead the job of the kingdom. Not like NATO where every country has their own military and has to help each other but as a federation where there is only one military.
Niels Anderson does a way better Job than me explaining it:
In the American special forces branch of the Navy, you receive extra Sausages, Eggs And Lard (S.E.A.L) in your rations, so these people are called "Seals".
Obviously, after a few years of eating so much extra greasy food, they're no longer capable of participating in military operations, so tend to retire and write books about what they did at work.
I think that's correct anyway - don't quote me on it.